In general, the production of piezoelectric resonators involves baking, molding, and polarization of a piezoelectric substrate 1 serving as a mother substrate (unit), as shown in FIG. 11. An electrode 2 with a constant thickness is formed by sputtering or vapor deposition on the entire front and back main surfaces of the piezoelectric substrate 1, and a plurality of vibrating electrodes are then formed by etching or the like. The piezoelectric substrate 1 is cut according to the vibrating electrodes, thereby fabricating the individual piezoelectric resonators.
FIG. 12 shows the distribution of frequency constants after the polarization of the piezoelectric substrate 1 serving as the mother substrate. In FIG. 12, the frequency constant (MHz·μm) is F×t (F: resonant frequency MHz of the piezoelectric substrate, and t: thickness μm of the piezoelectric substrate). As shown in FIG. 12, the frequency constants around the center of the piezoelectric substrate 1 are substantially equal. However, the frequency constants along the periphery of the piezoelectric substrate 1 are higher than those around the center. It is also clear from the distribution that the frequency constants have a gradient that gradually increases toward the outer periphery. Thus, the resonant frequencies within one piezoelectric substrate 1 are greatly different, causing characteristic variations among the individual piezoelectric resonators obtained from the piezoelectric substrate 1.
For example, when a piezoelectric resonator having vibrating electrodes 2a and 2b with a constant thickness shown in FIG. 13(a) is fabricated by cutting it out from a peripheral portion of the piezoelectric substrate 1 where the gradient of frequency constant is great (portion A in FIG. 11), the frequency constant changes in a surface direction of a piezoelectric substrate 1a serving as a child substrate, as shown in FIG. 13(b). When vibrations are generated between the vibrating electrodes 2a and 2b disposed on the front and back surfaces of the piezoelectric substrate 1a, unnecessary in-band vibrations R in a symmetric mode are generated, as shown in FIG. 14, and desired resonance characteristics cannot be achieved. As a result, piezoelectric resonators cut out from the peripheral portion of the piezoelectric substrate 1 shown in FIG. 11 must be discarded, resulting in a reduction in the substrate utilization rate (yield).
Patent Document 1 discloses a piezoelectric component having a piezoelectric resonator including a planar piezoelectric substrate and a pair of exciting electrodes formed on a pair of front and back main surfaces of the piezoelectric substrate, a first resin layer formed on the main surface to cover the exciting electrode, and a second resin layer formed to surround the first resin layer, thereby precisely adjusting the resonant frequency and obtaining the piezoelectric resonance component with stable characteristics.
However, in Patent Document 1, only the first resin layer covering the exciting electrode and the second resin layer surrounding the first resin layer are formed. When a frequency constant varies in the piezoelectric substrate, the first resin layer and the second resin layer can not reduce the frequency variation or suppress unnecessary vibrations generated due to the gradient of frequency constant.
Patent Document 2 discloses a method of adjusting the frequency of a piezoelectric resonator prepared by forming first and second vibrating electrodes on front and back major surfaces of a piezoelectric substrate, in which the thickness of the first vibrating electrode is greater than the thickness of the second vibrating electrode. The method includes thinning the first vibrating electrode or thickening the second vibrating electrode so that the thicknesses of the first and second vibrating electrodes become closer to each other, thereby achieving a desired frequency.
This can suppress the generation of in-band ripples while adjusting the frequency to a desired value.
In Patent Document 2, each of the first and second vibrating electrodes is processed to have a similar thickness in a whole area. When a frequency constant varies in the piezoelectric substrate, a precise resonant frequency cannot be achieved. Unnecessary vibrations generated by the gradient of frequency constant of the piezoelectric substrate cannot be suppressed.
FIG. 5 of Patent Document 3 discloses a piezoelectric resonator having a wedge-shaped piezoelectric substrate whose thickness changes with a constant gradient and a pair of drive electrodes facing each other, which are provided on two major sloping surfaces of the piezoelectric substrate, in which the thickness of the drive electrodes gradually increases toward the thinnest portion of the piezoelectric substrate. In this case, the thickness of the drive electrodes is changed to compensate for the tapering (sloping surfaces) of the piezoelectric substrate. That is, the thickness of the drive electrodes is gradually increased toward the thinnest portion of the piezoelectric substrate so that the total thickness of the piezoelectric substrate and the drive electrodes is the same in the longitudinal direction. This design prevents effects such as ripples induced by the tapering shape from appearing in the impedance characteristics.
However, even when the piezoelectric substrate has a constant thickness, the gradient of frequency constant of the piezoelectric substrate is generated. In the method described in Patent Document 3 in which the thickness of the piezoelectric substrate is changed with a constant gradient while the thickness of the electrodes has a gradient in the opposite direction, unnecessary vibrations resulting from the gradient of frequency constant cannot be effectively suppressed.    Patent Document 1: Japanese Unexamined Patent Application Publication No. 11-41051    Patent Document 2: Japanese Unexamined Patent Application Publication No. 2001-196883    Patent Document 3: Japanese Unexamined Patent Application Publication No. 2003-46364